Problem: Simplify the following expression: $\sqrt{99}+\sqrt{44}+\sqrt{275}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{99}+\sqrt{44}+\sqrt{275}$ $= \sqrt{9 \cdot 11}+\sqrt{4 \cdot 11}+\sqrt{25 \cdot 11}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{11}+\sqrt{4} \cdot \sqrt{11}+\sqrt{25} \cdot \sqrt{11}$ $= 3\sqrt{11}+2\sqrt{11}+5\sqrt{11}$ Finally, simplify by combining the terms. $= ( 3 + 2 + 5 )\sqrt{11} = 10\sqrt{11}$